Re: JUMP

That's still not the issue but since you mention it, it's rather useful to prove that 1 != 2. If you can't do that then all mathematics would fail, wouldn't it?!

P denotes the class of problems that can be solved in polynomial-time.
NP denotes the class of non-deterministic polynomial problems, meaning they could be solved in polynomial time using a non-deterministic Turing machine (if you have one of those, I'm ready to buy).

P is in the class of NP but not equal to it (most likely). Other parts of the NP class are the NP-Complete class and the class of incomplete problems.

When talking about problems, it's usually assumed to be decision problems (yes/no) but since a decision problem can be used to solve an optimization problem the optimization problem is in P if the decision problem is in P. You only use a method similar to the binary search method (which only adds a multiplicative factor O(c*log(n))) to convert the decision problem into an optimization problem.

Am I turning this into a CS thread now?

I'm sorta guessing you knew this already but in case someone else didn't..